Oh! I missed that you were asking about particular strengths. No, a consequential particular strength will reduce one die in that form. The book doesn't specify, but it'd be most consistent with the rest of the rules for the winner to choose which die.

Pretending for a moment the question was as first thought, if an NPC is down to one die in a form at 0, (e.g., d8 d4 takes damage and is now d6 d0) what happens if the form is damaged again?

(1) you can't go below zero so only the non-zero die is damage (in example now d4 d0).(2) if you can't do damage to two different dice because one is zero, do both to one die (so it's now, in example, d0 d0 - boom goes the NPC!)

Pretending for a moment the question was as first thought, if an NPC is down to one die in a form at 0, (e.g., d8 d4 takes damage and is now d6 d0) what happens if the form is damaged again?

I think it's just like players, so #1. If one of my dice is 0 from being injured, then the other one drops by one and that's all. Of course I'm close to being out so that's a pretty big stick when it comes to negotiating something else. If an NPC is at a d6 and d0 in manuevering, and is injured, it becomes d4 and d0. But, if they have d6 and d4 in action and are exhausted, then having a d4 and d0 there and d6 and d0 elsewhere means they are out because that's two d0s. But again, big stick so the GM might be "I want him in, how about this instead." or "Eh, this guy served his purpose and it's close to wrapping up, how about you cut off his arm and he flees instead?"